Re: (very) first draft of semantics available

On Feb 21, 2013, at 10:43 AM, Peter Patel-Schneider wrote:

> On Feb 20, 2013, at 1:45 PM, Peter Patel-Schneider wrote:
>  
> [...]
> 
> > > Externally-visible changes to the semantics:
> > >
> > > 1/ Ill-typed literals do not denote.  [...]
> > >
> > > 3/ Literal values need not be in the domain of discourse.
> > 
> > ?? They should be. Perhaps this is a slip, which I will correct.
> 
> For simple interpretations IL maps into IR.
> For D-interpretations IL is equated to L2V for recognized datatypes.
> 
> Why then, the note saying that D-interpretations don't contain all possible literal values and can be finite?  This is what caused my comment, and I didn't dig deep enough to see that it wasn't true.  

The idea (maybe I slipped in a few places) was to restrict all the mappings to the names in the vocabulary, which allows for finiteness (almost) everywhere. But the fact that you found it confusing makes me think this might be a losing strategy to adopt, and I should keep it simple and ignore finiteness in the main body of the text. 

> 
> The question of whether even simple interpretations are finite is confusing.  The first condition (please number them, by the way) says that every language-tagged literal

in the vocabulary.... (which might be finite, was the idea)

> has an IL mapping, which then must be a member of the domain, so this seems to show that simple interpretations are infinite.
> 
> > > 2/ LV is no longer used.  OWL uses LV from RDF, and so would have a
> > > dangling pointer.
> > 
> > LV is still *defined* to be the set of all values of actual literals in the universe. Its just not part of the basic structure. This should not change anything for OWL.  
> 
> Right, LV got moved from simple interpretations to D-interpretations, and I missed that.  However, I believe that its status changed.  LV used to just contain all the literal value spaces, but now it is defined as the union of the literal value spaces. 

Yes.

> This means that interpretations for different sets of datatypes are different, which may break extensibility for some languages.   OWL would certainly notice this change - an element of rdfs:Literal has to belong to at least one of the recognized datatypes.
> 
> So, if the only datatype is boolean (which, I admit, isn't possible for RDF or RDFS), then LV has precisely two elements.  This change also would be noticeable in some languages.

Ah, I wondered about that. OK then I will change that back to conform more closely to the 2004 story. However, it is then rather odd, since LV basically has no upper constraints on it. Ill-typed literals don't have a value, so LV could be the whole universe and it would not change anything in the RDF(S)-D space. It basically does not play any active role other than to be an extension for rdfs:Literal. In fact we can simply define it to be that :-)

> 
> > > Issues:
> > >
> > > 1/ Which interpretations can be used in entailment?
> > 
> > Um, all interpretations? That is, xxx-entailment means truth is preserved by all xxx-interpretations.
> > 
> > > There are no problems with using partial interpretations in RDF per se, I
> > > think, but consider
> > >   "24"^^xsd:integer rdf:type xsd:integer .
> > > under {xsd:integer}-RDF-interpretations.  Is this true in all such
> > > interpretations?
> > 
> > Right now, no, because the constraints on classes involving rdf:type are not introduced until we define RDFS. We could change this. Frankly I don't think it really matters, as we could define entailment regimes for just about any combination of the rdf: and/or rdfs: vocabularies and/or datatyping.
> 
> > It does seem natural since rdf:type is in the rdf namespace, I agree.
> 
> Yes.

Yes, I have come to agree. I will reorganize this to fit the namespace structure better. 

> 
> My confusion had to do with non-denoting well-formed literals, which don't appear to be possible, but the document is very confusing on this point.
> 
> [...]
> 
> > > 2/ The empty graph is not true in all simple interpretations.
> > 
> > Seems to me it is. Simple interpretation conditions say the only way a graph can be false is by having a false triple, so empty must be true, no?
> > 
> > > Does this matter?
> > 
> > It would, yes.
> 
> Consider a simple interpretation where IL("ss"^^xsd:integer)="tt", which appears to be possible. This conflicts with the semantic conditions for ground graphs. 

Ah, I see your point. Yes, the two conditions on literals should be stated as part of the definition of simple interpretation. I will fix this. 

> From this, I leapt to that everything would be false, but I see that this doesn't follow.

> 
> Nevertheless, this does seem to be very strange.

Its an error of presentation, my bad. 

> 
> > > 3/ Are rdf:XMLLiteral and rdf:HTML required for RDF interpretations?
> > 
> > No. We could change this, if you think it would be better if they were. Again, perhaps they should be since these are in the rdf: namespace.
> 
> Huh? 

AArgh, never reply to emails when you are tired. Yes you are right, sorry. 

> Aren't RDF-interpretations defined as {rdf:XMLLiteral, rdf:HTML, rdf:langString, xsd:string}-interpretations.
> 
> My question was rather whether this should be so.

Well, they are in the rdf: space, so why not? (We could define two layers of RDF interpretations, one with and one without, but it starts to get bloated with distinctions pretty quickly.)

> > > Technical Suggestions
> 
> > > 3/ Fixes for datatypes
> > > - RDF - if v is in the value set of D then <v,D> in IEXT(I(rdf:type))
> > > NOTE:  This makes the domain of discourse for all D-interpretations infinite.
> > 
> > Does this bother you? We could keep D-interpretations finite by only requiring this condition for values denoted by a literal in the vocabulary.
> 
> See above.  It appears that all interpretations are infinite.
> 
> > I find myself pulled to conflicting directions over this (and related) issues. On the one hand, the simplest way to state a lot of these conditons is to state them for *all* values (as here) and similarly to say that all interpretations are mappings from *all* IRIs, and so on. This avoids a host of verbiage and fussing over exact domains of mappings, and qualifications about being in the vocabulary and so on, none of which is really germane and just clutters up the exposition for the average reader. But on the other hand, this forces things to be infinite that could in fact be finite and everything still work, and this finiteness is important for another class of reader. I would hope that this other class of reader, competent in model theory, would find it obvious that all of this can be restricted to much smaller structures which are defined only on the vocabulary actually in use in any given case, and that these can be finite. Can we rely on this, do you think? Or are people going to say that since the simple statement is labelled 'normative', that RDF structures are *required* to be infinite?
> > 
> > My inclination is to use the simple presentation in the body of the text, but have notes linked to an appendix which explains the restriction-to-actual-vocabulary variation and why it allows for finite interpretation structures.
> > 
> > Comments on this idea?
> > 
> > 
> > > - RDFS - if D is a datatype then <D,I(rdfs:Datatype)> in IEXT(I(rdf:type))
> > >
> > > Technical wording changes:
> 
> > > 1/ Rewrites for partial interpretations, including:
> > > - simple semantic mapping for literals is partial
> > > - simple semantic mapping for a triple is false if any literal in it does
> > > not denote
> > 
> > We have both of these now, no?
> 
> Not in the definition of simple interpretations, where it should be, I think.

Yes, I agree.

> 
> > > - do all IRIs denote?
> > 
> > Yes.
> > 
> > > If so there are lots of places where the wording
> > > indicates that they might not.
> > 
> > The basic rules require that the IR mapping is total. Does that not cover it?
> 
> Why then "Turned around, this means that in order for a graph to be true, all the *IRI* and literal nodes in it must refer to something in the world being described"?  This is confusing.

Ah, I see what your concern is here. OK, let me try to find a better way to phrase this (like, maybe, deleting it altogether.) 

> 
> > > If not, then this should be made clear how
> > > they might not.
> 
> > > Other Suggestions
> 
> [...]
> 
> > > 2/ All simple interpretations used to be [in]finite, so the note about
> > > finiteness of D-interpretations is a bit awkward.
> > 
> > I am assuming as an editorial stance that this document should not presume that one has read the 2004 specs first, so might need to (re)state things which have been obvious in the past.
> 
> > > 5/ Remove stuff about OOP.
> > 
> > I want this in there somewhere, as this has given rise to a lot of confusion in the past. (And still does, in fact.) Maybe in the beginner's guide.
> 
> I think that concepts would be a much better place for it.

Good point. I agree. 

> > > 6/ Remove note on inference rules, which even uses a particular meaning for
> > > "inference rule".
> > 
> > Hmm. What do you feel about restating all these conditions as rules (strike "inference") ? It could be done and a lot of readers would find it easier to follow.
> 
> I don't know what this means.  My comment was about the note on "inference rules".

The 'technical note' in section 4.1 talking about the RDFS semantic conditions table? I was talking about those conditions. If you mean some other place where "inference rules" are mentioned, then we are at cross purposes. 

I should probably avoid the term "inference rule" and just say "rule", yes. 

> > > Other Wording changes:
> 
> [...]
> 
> > > 3/ It is unfortunate that vocabulary is used in two senses: a) the domain of
> > > IS, and b) vocabulary interpretations.
> > 
> > Yes. I have a thought to try out on you, which is to eliminate the first sense of vocabulary altogether, and say that all interpretations are defined on *all* IRIs. So the whole concept of an interpretation *of a vocabulary* is simplified to not speak of vocabularies. The entire Web, past present and future, is one giant vocabulary (or, if you prefer, one giant FO language.) Of course they are all then infinite, but (as will be pointed out in a technical note) the actual interpretation structure, including the universe, can still be finite, and it is only necessary to define the interpretation mapping for the IRIs (and literals) which are actually in use.
> > 
> > Comments on this idea? Seems to me it will make life easier for the folk who are struggling with model theory in the first place, and will be an obvious hack for those who are familiar with the basic ideas and might be concerned about finiteness. The whole "of a vocabulary V" business does not really play any useful role in the 2004 specs. And this would bypass a whole pointless discussion about the infinitude of the rdf:_n container vocabulary, for example.

Comments on the above? 

Pat

> 
> [...]
> 
> peter
> 

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Received on Thursday, 21 February 2013 18:32:10 UTC